Nonlinear Finite Element Models for Solids and Structures

Cálculo no lineal de sólidos y estructuras mediante elementos finitos

10 Jan 2014

Lecturers

Background and objectives of course

The course consists of 13 2h lessons. Out of these 10 will be dedicated to lectures and 3 will be dedicated to applications. In the lectures the key concepts for the mathematical and numerical models will be explained. Practical indications for solving the exercises with finite element program FEAP will be also given. The Application lessons will include full discussions of real world applications of advanced finite element models, within research projects or technological development projects.

Students are expected to have a good basic background in finite elements, for which in principle the course given in the 1st semester "Finite Element Method / Método de los elementos finitos" is required. In the first semester course also the FEAP finite element program is employed, which is a practical requirement for this course.

Documentation will be provided in the way of presentation notes and papers. A binary version of FEAP will be provided for use of the students within this course.

In some lessons a homework assignment will be given to students who must complete the work individually and return the worked out report through the moodle course site. A total of 8 homework exercises will be proposed. Additionally the students will be asked to develop an individual final project for the course. These final projects will be presented by the students to the whole class in a special workshop.

Program and calendar of lessons

  1. Introduction to nonlinear problems  (13 feb 2014, JG)
    Nonlinear behaviour in mechanical and structural applications. Detailed analysis of basic examples for understanding the nature of the problems and of the finite element solutions. Sources of nonlinear behaviour in solids and structures. Required features of nonlinear FE programs. State of the art in advanced applications of FE to engineering problems.
  2. Concepts in nonlinear continuum mechanics (1) (20 feb 2014, JG)
    Large strain formulation. Kinematics. Strain tensors. Stress tensors.
  3. Concepts in nonlinear continuum mechanics (2) (27 feb 2014, JG)
    Balance principles and conservation theorems. Thermodynamics. Constitutive equations of materials: general principles.
  4. Constitutive models for plasticity and viscoplasticity  (06 mar 2014, SB)
    Elastic-plastic models. Finite strain elastoplasticity. Integration of the equations of plasticity. Tangent elastoplastic matrix. Algorithmic consistent tangent. Viscoplasticity. Applications.
  5. Constitutive models for gelogical and cohesive-frictional materials (13 mar 2014, FM)
    Material properties and models. Concrete: properties and models in compression and tension.
  6. Constitutive models for nonlinear elasticity and viscoelasticity  (20 mar 2014, SB)
    Models for incremental hypoelasticity. Hyperelastic models. Elastomers. Anisotropy. Soft biological tissue. Viscoelasticity.
  7. Formulation of the discrete nonlinear equations (27 mar 2014, JG)
    Total Lagrangian and updated Lagrangian weak formulations. Linearization of the weak formulation. Interpolation of strains. Evaluation of internal forces. Tangent stiffness matrix. Finite element equations.
  8. Solution algorithms for the nonlinear equations  (03 apr 2014, JG)
    Equilibrium solutions and implicit time integration. Linearization and iterative solutions. Line search for acceleration convergence. Continuation methods: arc-length. Stability.
  9. Mixed and hybrid elements for nonlinear probelms (10 apr 2014, FG)
    Enhanced assumed strains. Elements u-p-theta. Finite elements for incompressible Navier-Stokes flow.
  10. Models for nonlinear dynamics  (24 apr 2014, JG)
    Explicit methods. Implicit time integration. Contact and impact. Rigid bodies. Constraints. Energy-momentum method.
  11. Final course projects  (assignment and discussion: 08, 22 may 2014, All; presentation: TBD)
    Workshops for discussion and assignement of final course projects, and presentation of projects by each students. Projects will be carried out individually.
  12. Isogeometric Analysis (integrating FE with NURBS computational geometry)  (date TBD, PA)
  13. Application: Industrial problems  (29 may 2014, FM)

Bibliography

Grading Criteria

For passing the course it will be required to assist to the lectures and complete the homework assignments, as well as the final course project.

The grades will be based on three criteria:

  1. Attendance and participation in classes (15% of grades, with a minimum attendance of 70% of classes)
  2. Assignments and exercises (50% of grades)
  3. Final coursework: report, presentation and discussion (35% of grades)